Lazy and Fast Greedy MAP Inference for Determinantal Point Process
This work provides an incremental improvement for researchers and practitioners in machine learning who need efficient algorithms for selecting diverse items using DPPs.
The paper tackles the problem of MAP inference for determinantal point processes (DPPs) by combining lazy and fast greedy algorithms, which were previously considered incompatible, resulting in a new algorithm that achieves almost the same time complexity as the best current method and runs faster in practice.
The maximum a posteriori (MAP) inference for determinantal point processes (DPPs) is crucial for selecting diverse items in many machine learning applications. Although DPP MAP inference is NP-hard, the greedy algorithm often finds high-quality solutions, and many researchers have studied its efficient implementation. One classical and practical method is the lazy greedy algorithm, which is applicable to general submodular function maximization, while a recent fast greedy algorithm based on the Cholesky factorization is more efficient for DPP MAP inference. This paper presents how to combine the ideas of "lazy" and "fast", which have been considered incompatible in the literature. Our lazy and fast greedy algorithm achieves almost the same time complexity as the current best one and runs faster in practice. The idea of "lazy + fast" is extendable to other greedy-type algorithms. We also give a fast version of the double greedy algorithm for unconstrained DPP MAP inference. Experiments validate the effectiveness of our acceleration ideas.